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Principal currents for a pair of unitary operators

About this Title

Joel Pincus and Shao Jie Zhou

Publication: Memoirs of the American Mathematical Society
Publication Year 1994: Volume 109, Number 522
ISBNs: 978-0-8218-2609-6 (print); 978-1-4704-0099-6 (online)
MathSciNet review: 1243584
MSC: Primary 47-02; Secondary 30E25, 47A45, 47B20

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Table of Contents


  • 0. Introduction
  • 1. The geometry associated with eigenvalues
  • 2. The dilation space solution of the symbol Riemann Hilbert problem
  • 3. The principal current for the operator-tuple $\{P_1, P_2, W_1, W_2\}$
  • 4. Estimates
  • 5. The criterion for eigenvalues
  • 6. The $N(\omega )$ operator
  • 7. The characteristic operator function of $T_1$
  • 8. Localization and the “cut-down” property
  • 9. The joint essential spectrum
  • 10. Singular integral representations
  • 11. Toeplitz operators with unimodular symbols
  • 12. $C_{11}$-contraction operators with (1,1) deficiency indices
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